Problem: Express your answer as a mixed number simplified to lowest terms. $7\dfrac{2}{5}-2\dfrac{4}{9} = {?}$
Answer: Find a common denominator for the fractions: $= {7\dfrac{18}{45}}-{2\dfrac{20}{45}}$ Convert ${7\dfrac{18}{45}}$ to ${6 + \dfrac{45}{45} + \dfrac{18}{45}}$ So the problem becomes: ${6\dfrac{63}{45}}-{2\dfrac{20}{45}}$ Separate the whole numbers from the fractional parts: $= {6} + {\dfrac{63}{45}} - {2} - {\dfrac{20}{45}}$ Bring the whole numbers together and the fractions together: $= {6} - {2} + {\dfrac{63}{45}} - {\dfrac{20}{45}}$ Subtract the whole numbers: $=4 + {\dfrac{63}{45}} - {\dfrac{20}{45}}$ Subtract the fractions: $= 4+\dfrac{43}{45}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{43}{45}$